Special Forms A combination that is not a call expression is a special form: Evaluation: • if expression: (if <predicate> <consequent> <alternative>) (1) Evaluate the predicate expression • and and or : (and <e1> ... <en>), (or <e1> ... <en>) (2) Evaluate either • Binding symbols: (define <symbol> <expression>) the consequent or alternative > (define pi 3.14) The symbol “pi” is bound to 3.14 in the > (* pi 2) global frame 6.28 7
Special Forms A combination that is not a call expression is a special form: Evaluation: • if expression: (if <predicate> <consequent> <alternative>) (1) Evaluate the predicate expression • and and or : (and <e1> ... <en>), (or <e1> ... <en>) (2) Evaluate either • Binding symbols: (define <symbol> <expression>) the consequent or alternative • New procedures: (define (<symbol> <formal parameters>) <body>) > (define pi 3.14) The symbol “pi” is bound to 3.14 in the > (* pi 2) global frame 6.28 7
Special Forms A combination that is not a call expression is a special form: Evaluation: • if expression: (if <predicate> <consequent> <alternative>) (1) Evaluate the predicate expression • and and or : (and <e1> ... <en>), (or <e1> ... <en>) (2) Evaluate either • Binding symbols: (define <symbol> <expression>) the consequent or alternative • New procedures: (define (<symbol> <formal parameters>) <body>) > (define pi 3.14) The symbol “pi” is bound to 3.14 in the > (* pi 2) global frame 6.28 > (define (abs x) (if (< x 0) (- x) x)) > (abs -3) 3 7
Special Forms A combination that is not a call expression is a special form: Evaluation: • if expression: (if <predicate> <consequent> <alternative>) (1) Evaluate the predicate expression • and and or : (and <e1> ... <en>), (or <e1> ... <en>) (2) Evaluate either • Binding symbols: (define <symbol> <expression>) the consequent or alternative • New procedures: (define (<symbol> <formal parameters>) <body>) > (define pi 3.14) The symbol “pi” is bound to 3.14 in the > (* pi 2) global frame 6.28 > (define (abs x) A procedure is created and bound to the (if (< x 0) symbol “abs” (- x) x)) > (abs -3) 3 7
Special Forms A combination that is not a call expression is a special form: Evaluation: • if expression: (if <predicate> <consequent> <alternative>) (1) Evaluate the predicate expression • and and or : (and <e1> ... <en>), (or <e1> ... <en>) (2) Evaluate either • Binding symbols: (define <symbol> <expression>) the consequent or alternative • New procedures: (define (<symbol> <formal parameters>) <body>) > (define pi 3.14) The symbol “pi” is bound to 3.14 in the > (* pi 2) global frame 6.28 > (define (abs x) A procedure is created and bound to the (if (< x 0) symbol “abs” (- x) x)) > (abs -3) 3 7
Special Forms A combination that is not a call expression is a special form: Evaluation: • if expression: (if <predicate> <consequent> <alternative>) (1) Evaluate the predicate expression • and and or : (and <e1> ... <en>), (or <e1> ... <en>) (2) Evaluate either • Binding symbols: (define <symbol> <expression>) the consequent or alternative • New procedures: (define (<symbol> <formal parameters>) <body>) > (define pi 3.14) The symbol “pi” is bound to 3.14 in the > (* pi 2) global frame 6.28 > (define (abs x) A procedure is created and bound to the (if (< x 0) symbol “abs” (- x) x)) > (abs -3) 3 (Demo) 7
Scheme Interpreters (Demo)
Lambda Expressions
Lambda Expressions Lambda expressions evaluate to anonymous procedures 10
Lambda Expressions Lambda expressions evaluate to anonymous procedures (lambda (<formal-parameters>) <body>) 10
Lambda Expressions Lambda expressions evaluate to anonymous procedures λ (lambda (<formal-parameters>) <body>) 10
Lambda Expressions Lambda expressions evaluate to anonymous procedures λ (lambda (<formal-parameters>) <body>) Two equivalent expressions: (define (plus4 x) (+ x 4)) (define plus4 (lambda (x) (+ x 4))) 10
Lambda Expressions Lambda expressions evaluate to anonymous procedures λ (lambda (<formal-parameters>) <body>) Two equivalent expressions: (define (plus4 x) (+ x 4)) (define plus4 (lambda (x) (+ x 4))) An operator can be a call expression too: 10
Lambda Expressions Lambda expressions evaluate to anonymous procedures λ (lambda (<formal-parameters>) <body>) Two equivalent expressions: (define (plus4 x) (+ x 4)) (define plus4 (lambda (x) (+ x 4))) An operator can be a call expression too: ((lambda (x y z) (+ x y (square z))) 1 2 3) 10
Lambda Expressions Lambda expressions evaluate to anonymous procedures λ (lambda (<formal-parameters>) <body>) Two equivalent expressions: (define (plus4 x) (+ x 4)) (define plus4 (lambda (x) (+ x 4))) An operator can be a call expression too: ((lambda (x y z) (+ x y (square z))) 1 2 3) Evaluates to the x+y+z 2 procedure 10
Lambda Expressions Lambda expressions evaluate to anonymous procedures λ (lambda (<formal-parameters>) <body>) Two equivalent expressions: (define (plus4 x) (+ x 4)) (define plus4 (lambda (x) (+ x 4))) An operator can be a call expression too: ((lambda (x y z) (+ x y (square z))) 1 2 3) 12 Evaluates to the x+y+z 2 procedure 10
Sierpinski's Triangle (Demo)
More Special Forms
Cond & Begin 13
Cond & Begin The cond special form that behaves like if-elif-else statements in Python 13
Cond & Begin The cond special form that behaves like if-elif-else statements in Python if x > 10: print('big') elif x > 5: print('medium') else : print('small') 13
Cond & Begin The cond special form that behaves like if-elif-else statements in Python if x > 10: print('big') ( cond ((> x 10) (print 'big)) elif x > 5: ((> x 5) (print 'medium)) print('medium') ( else (print 'small))) else : print('small') 13
Cond & Begin The cond special form that behaves like if-elif-else statements in Python if x > 10: print('big') ( cond ((> x 10) (print 'big)) ( cond ((> x 10) 'big) elif x > 5: ((> x 5) (print 'medium)) ((> x 5) 'medium) print('medium') ( else (print 'small))) ( else 'small)) else : print('small') 13
Cond & Begin The cond special form that behaves like if-elif-else statements in Python if x > 10: (print print('big') ( cond ((> x 10) (print 'big)) ( cond ((> x 10) 'big) elif x > 5: ((> x 5) (print 'medium)) ((> x 5) 'medium) print('medium') ( else (print 'small))) ) ( else 'small)) else : print('small') 13
Cond & Begin The cond special form that behaves like if-elif-else statements in Python if x > 10: (print print('big') ( cond ((> x 10) (print 'big)) ( cond ((> x 10) 'big) elif x > 5: ((> x 5) (print 'medium)) ((> x 5) 'medium) print('medium') ( else (print 'small))) ) ( else 'small)) else : print('small') The begin special form combines multiple expressions into one expression 13
Cond & Begin The cond special form that behaves like if-elif-else statements in Python if x > 10: (print print('big') ( cond ((> x 10) (print 'big)) ( cond ((> x 10) 'big) elif x > 5: ((> x 5) (print 'medium)) ((> x 5) 'medium) print('medium') ( else (print 'small))) ) ( else 'small)) else : print('small') The begin special form combines multiple expressions into one expression if x > 10: print('big') print('guy') else : print('small') print('fry') 13
Cond & Begin The cond special form that behaves like if-elif-else statements in Python if x > 10: (print print('big') ( cond ((> x 10) (print 'big)) ( cond ((> x 10) 'big) elif x > 5: ((> x 5) (print 'medium)) ((> x 5) 'medium) print('medium') ( else (print 'small))) ) ( else 'small)) else : print('small') The begin special form combines multiple expressions into one expression ( cond ((> x 10) ( begin (print 'big) (print 'guy))) if x > 10: ( else ( begin (print 'small) (print 'fry)))) print('big') print('guy') else : print('small') print('fry') 13
Cond & Begin The cond special form that behaves like if-elif-else statements in Python if x > 10: (print print('big') ( cond ((> x 10) (print 'big)) ( cond ((> x 10) 'big) elif x > 5: ((> x 5) (print 'medium)) ((> x 5) 'medium) print('medium') ( else (print 'small))) ) ( else 'small)) else : print('small') The begin special form combines multiple expressions into one expression ( cond ((> x 10) ( begin (print 'big) (print 'guy))) if x > 10: ( else ( begin (print 'small) (print 'fry)))) print('big') print('guy') else : ( if (> x 10) ( begin print('small') (print 'big) print('fry') (print 'guy)) ( begin (print 'small) (print 'fry))) 13
Let Expressions The let special form binds symbols to values temporarily; just for one expression 14
Let Expressions The let special form binds symbols to values temporarily; just for one expression a = 3 b = 2 + 2 c = math.sqrt(a * a + b * b) 14
Let Expressions The let special form binds symbols to values temporarily; just for one expression a = 3 b = 2 + 2 c = math.sqrt(a * a + b * b) a and b are still bound down here 14
Let Expressions The let special form binds symbols to values temporarily; just for one expression a = 3 ( define c ( let ((a 3) b = 2 + 2 (b (+ 2 2))) c = math.sqrt(a * a + b * b) (sqrt (+ (* a a) (* b b))))) a and b are still bound down here 14
Let Expressions The let special form binds symbols to values temporarily; just for one expression a = 3 ( define c ( let ((a 3) b = 2 + 2 (b (+ 2 2))) c = math.sqrt(a * a + b * b) (sqrt (+ (* a a) (* b b))))) a and b are still bound down here a and b are not bound down here 14
Lists
Scheme Lists
Scheme Lists In the late 1950s, computer scientists used confusing names
Scheme Lists In the late 1950s, computer scientists used confusing names • cons : Two-argument procedure that creates a linked list
Scheme Lists In the late 1950s, computer scientists used confusing names • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list
Scheme Lists In the late 1950s, computer scientists used confusing names • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list • cdr : Procedure that returns the rest of a list
Scheme Lists In the late 1950s, computer scientists used confusing names • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list • cdr : Procedure that returns the rest of a list • nil : The empty list
Scheme Lists In the late 1950s, computer scientists used confusing names (cons 2 nil) 2 nil • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list • cdr : Procedure that returns the rest of a list • nil : The empty list
Scheme Lists In the late 1950s, computer scientists used confusing names (cons 2 nil) 2 nil • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list 2 • cdr : Procedure that returns the rest of a list • nil : The empty list
Scheme Lists In the late 1950s, computer scientists used confusing names (cons 2 nil) 2 nil • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list 2 • cdr : Procedure that returns the rest of a list • nil : The empty list Important! Scheme lists are written in parentheses with elements separated by spaces
Scheme Lists In the late 1950s, computer scientists used confusing names (cons 2 nil) 2 nil • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list 2 • cdr : Procedure that returns the rest of a list • nil : The empty list Important! Scheme lists are written in parentheses with elements separated by spaces (cons 2 nil) 2
Scheme Lists In the late 1950s, computer scientists used confusing names (cons 2 nil) 2 nil • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list 2 • cdr : Procedure that returns the rest of a list • nil : The empty list Important! Scheme lists are written in parentheses with elements separated by spaces > (cons 1 ) (cons 2 nil) 2 1
Scheme Lists In the late 1950s, computer scientists used confusing names (cons 2 nil) 2 nil • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list 2 • cdr : Procedure that returns the rest of a list • nil : The empty list Important! Scheme lists are written in parentheses with elements separated by spaces > (cons 1 ) (cons 2 nil) 2 1 (1 2)
Scheme Lists In the late 1950s, computer scientists used confusing names (cons 2 nil) 2 nil • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list 2 • cdr : Procedure that returns the rest of a list • nil : The empty list Important! Scheme lists are written in parentheses with elements separated by spaces > (cons 1 ) (cons 2 nil) 2 1 (1 2) > (define x (cons 1 (cons 2 nil))
Scheme Lists In the late 1950s, computer scientists used confusing names (cons 2 nil) 2 nil • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list 2 • cdr : Procedure that returns the rest of a list • nil : The empty list Important! Scheme lists are written in parentheses with elements separated by spaces > (cons 1 ) (cons 2 nil) 2 1 (1 2) > (define x (cons 1 (cons 2 nil)) > x
Scheme Lists In the late 1950s, computer scientists used confusing names (cons 2 nil) 2 nil • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list 2 • cdr : Procedure that returns the rest of a list • nil : The empty list Important! Scheme lists are written in parentheses with elements separated by spaces > (cons 1 ) (cons 2 nil) 2 1 (1 2) > (define x (cons 1 (cons 2 nil)) > x (1 2)
Scheme Lists In the late 1950s, computer scientists used confusing names (cons 2 nil) 2 nil • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list 2 • cdr : Procedure that returns the rest of a list • nil : The empty list Important! Scheme lists are written in parentheses with elements separated by spaces > (cons 1 ) (cons 2 nil) 2 1 (1 2) > (define x (cons 1 (cons 2 nil)) > x (1 2) > (car x)
Scheme Lists In the late 1950s, computer scientists used confusing names (cons 2 nil) 2 nil • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list 2 • cdr : Procedure that returns the rest of a list • nil : The empty list Important! Scheme lists are written in parentheses with elements separated by spaces > (cons 1 ) (cons 2 nil) 2 1 (1 2) > (define x (cons 1 (cons 2 nil)) > x (1 2) > (car x) 1
Scheme Lists In the late 1950s, computer scientists used confusing names (cons 2 nil) 2 nil • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list 2 • cdr : Procedure that returns the rest of a list • nil : The empty list Important! Scheme lists are written in parentheses with elements separated by spaces > (cons 1 ) (cons 2 nil) 2 1 (1 2) > (define x (cons 1 (cons 2 nil)) > x (1 2) > (car x) 1 > (cdr x)
Scheme Lists In the late 1950s, computer scientists used confusing names (cons 2 nil) 2 nil • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list 2 • cdr : Procedure that returns the rest of a list • nil : The empty list Important! Scheme lists are written in parentheses with elements separated by spaces > (cons 1 ) (cons 2 nil) 2 1 (1 2) > (define x (cons 1 (cons 2 nil)) > x (1 2) > (car x) 1 > (cdr x) (2)
Scheme Lists In the late 1950s, computer scientists used confusing names (cons 2 nil) 2 nil • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list 2 • cdr : Procedure that returns the rest of a list • nil : The empty list Important! Scheme lists are written in parentheses with elements separated by spaces > (cons 1 ) (cons 2 nil) 2 1 (1 2) > (define x (cons 1 (cons 2 nil)) > x (1 2) > (car x) 1 > (cdr x) (2) > (cons 1 (cons 2 (cons 3 (cons 4 nil))))
Scheme Lists In the late 1950s, computer scientists used confusing names (cons 2 nil) 2 nil • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list 2 • cdr : Procedure that returns the rest of a list • nil : The empty list Important! Scheme lists are written in parentheses with elements separated by spaces > (cons 1 ) (cons 2 nil) 2 1 (1 2) > (define x (cons 1 (cons 2 nil)) > x (1 2) > (car x) 1 > (cdr x) (2) > (cons 1 (cons 2 (cons 3 (cons 4 nil)))) 1 2 3 4
Scheme Lists In the late 1950s, computer scientists used confusing names (cons 2 nil) 2 nil • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list 2 • cdr : Procedure that returns the rest of a list • nil : The empty list Important! Scheme lists are written in parentheses with elements separated by spaces > (cons 1 ) (cons 2 nil) 2 1 (1 2) > (define x (cons 1 (cons 2 nil)) > x (1 2) > (car x) 1 > (cdr x) (2) > (cons 1 (cons 2 (cons 3 (cons 4 nil)))) 1 2 3 4 (1 2 3 4)
Scheme Lists In the late 1950s, computer scientists used confusing names (cons 2 nil) 2 nil • cons : Two-argument procedure that creates a linked list • car : Procedure that returns the first element of a list 2 • cdr : Procedure that returns the rest of a list • nil : The empty list Important! Scheme lists are written in parentheses with elements separated by spaces > (cons 1 ) (cons 2 nil) 2 1 (1 2) > (define x (cons 1 (cons 2 nil)) > x (1 2) > (car x) 1 > (cdr x) (2) > (cons 1 (cons 2 (cons 3 (cons 4 nil)))) 1 2 3 4 (1 2 3 4) (Demo)
Symbolic Programming
Symbolic Programming 18
Symbolic Programming Symbols normally refer to values; how do we refer to symbols? 18
Symbolic Programming Symbols normally refer to values; how do we refer to symbols? > (define a 1) 18
Symbolic Programming Symbols normally refer to values; how do we refer to symbols? > (define a 1) > (define b 2) 18
Symbolic Programming Symbols normally refer to values; how do we refer to symbols? > (define a 1) > (define b 2) > (list a b) 18
Symbolic Programming Symbols normally refer to values; how do we refer to symbols? > (define a 1) > (define b 2) > (list a b) (1 2) 18
Symbolic Programming Symbols normally refer to values; how do we refer to symbols? > (define a 1) > (define b 2) No sign of “a” and “b” in the > (list a b) resulting value (1 2) 18
Symbolic Programming Symbols normally refer to values; how do we refer to symbols? > (define a 1) > (define b 2) No sign of “a” and “b” in the > (list a b) resulting value (1 2) Quotation is used to refer to symbols directly in Lisp. 18
Symbolic Programming Symbols normally refer to values; how do we refer to symbols? > (define a 1) > (define b 2) No sign of “a” and “b” in the > (list a b) resulting value (1 2) Quotation is used to refer to symbols directly in Lisp. > (list 'a 'b) 18
Symbolic Programming Symbols normally refer to values; how do we refer to symbols? > (define a 1) > (define b 2) No sign of “a” and “b” in the > (list a b) resulting value (1 2) Quotation is used to refer to symbols directly in Lisp. > (list 'a 'b) (a b) 18
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